function [vfb,wfb,cy1fb,cy2fb,w_conv]=Intconv(gamma,betta,delta,n,pi1,pi2,v1aut)

% log case
cy1fb=((delta*(1+n))/(betta+delta*(1+n))); % total young consumption as rate of total endowment
cy2fb=((delta*(1+n))/(betta+delta*(1+n)));

co1fb = 1-cy1fb;   % consumption of old state 1
co2fb = 1-cy2fb;   % consumption of old state 2

vfb = (pi1*((1+n)*utility(cy1fb,gamma)+(betta/delta)*utility(co1fb,gamma))...
      +pi2*((1+n)*utility(cy2fb,gamma)+(betta/delta)*utility(co2fb,gamma)))./(1-delta*(1+n)); % expected per-period utility of central planner in the first-best 

wfb = pi1*utility(co1fb,gamma)+pi2*utility(co2fb,gamma); % expected promised utility in the first-best 

w_conv = (1/betta)*(v1aut-utility(cy1fb,gamma)); % theoretical convergence of expected promised in state 1
end
